Which assumption in MANOVA extends the idea of homogeneity of variance to multiple dependent variables by requiring equal variances and roughly equal covariances across groups?

Which assumption in MANOVA extends the idea of homogeneity of variance to multiple dependent variables by requiring equal variances and roughly equal covariances across groups?

• A. Homogeneity of variance
• B. Homogeneity of covariance matrices
• C. Normality
• D. Homogeneity of regression slopes

Answer: (B)

In MANOVA, the assumption you’re dealing with is that the way the dependent variables relate to each other is the same across groups. This extends the idea of equal variances to multiple dependent variables by requiring the covariance matrices to be the same in each group. In other words, you want both the variances to be similar and the covariances among the dependent variables to be roughly the same across groups. When this covariance structure is equal across groups, we say the covariance matrices are homogeneous. This uniform pattern supports the distributional assumptions behind MANOVA tests like Wilks’ lambda. A common way to assess this is Box’s M test. Other options aren’t addressing the multivariate covariance structure: normality concerns the overall distribution shape within groups, not the equality of covariance patterns across groups, and homogeneity of variance is the univariate version for a single dependent variable, not the combined covariance structure. Homogeneity of regression slopes is about covariate effects and not the covariance matrices of the dependent variables.

In MANOVA, the assumption you’re dealing with is that the way the dependent variables relate to each other is the same across groups. This extends the idea of equal variances to multiple dependent variables by requiring the covariance matrices to be the same in each group. In other words, you want both the variances to be similar and the covariances among the dependent variables to be roughly the same across groups. When this covariance structure is equal across groups, we say the covariance matrices are homogeneous. This uniform pattern supports the distributional assumptions behind MANOVA tests like Wilks’ lambda. A common way to assess this is Box’s M test. Other options aren’t addressing the multivariate covariance structure: normality concerns the overall distribution shape within groups, not the equality of covariance patterns across groups, and homogeneity of variance is the univariate version for a single dependent variable, not the combined covariance structure. Homogeneity of regression slopes is about covariate effects and not the covariance matrices of the dependent variables.